Attack of the Glib Reductionists

Douglas Hofstadter, pudding and pie,
Kissed the integers and made them cry.
But when the infinities came out to play,
Douglas Hofstadter ran away.
Adapted by Peter Van Roy from Georgie Porgie.
Several popular authors are using specious arguments to speculate wildly and irresponsibly about the human mind. Douglas Hofstadter has written popular speculative books such as Gödel, Escher, Bach: An Eternal Golden Braid and I Am a Strange Loop. He is fond of thought experiments that cannot be carried out in practice, such as “What if all the neurons in your brain would be replaced one by one by synthetic equivalents?” or “What if a teleportation device were to make an exact duplicate of you?”.1 He then purports to make deep and profound conclusions about consciousness and free will from such thought experiments. But they are fundamentally flawed: they are so far removed from our abilities and knowledge that it may very well be that they cannot be carried out or that carrying them out would require completely new understanding.2

John Searle's Chinese Room thought experiment has the same flaw and so does Raymond Kurzweil's breathless prediction of the Singularity. It is like jumping six inches in the air and then deducing from this what space travel might be like.3 In the year 1957, people told of the power of laptop computers in 2007 might very well think that they would be intelligent, which is far from the case. Google's search engine uses enormously more computing power than a laptop and can answer many profound questions, but it is clearly an idiot savant: it shows no glimmering of intelligence. The barrier between the fundamental equations of physics and human experience is so wide that we cannot make any firm conclusions about it without actually traversing it. Per Brand calls it an example of an infinity barrier.4. Glibly jumping over such a barrier as if it did not exist leads only to wild speculation, not to firm knowledge.

The outer limits of human intelligence are greatly underestimated. Consider a world-class mathematician or musician. This person starts when young with a promising innate ability and works hard over several decades to improve that ability. Over a long period of time, the conscious mind of the person is single-mindedly dedicated to this task. The final result of this effort is that the ability has progressed beyond the capacity of most people to imagine the level it has attained. Without some real understanding of how to quantify this level, it is ridiculous to pretend that it can easily be jumped over.


  1. Recent work on quantum teleportation supports the conclusion that quantum states can be transported but not copied. That is, teleporting a quantum state will invariably destroy the initial state. This means that teleportation of a person is theoretically possible but creating an exact copy of a person is not. This implies that it is not possible to describe a quantum state in classical terms, e.g., write it down as a finite bit vector. If this is true, creating a synthetic neuron with the same quantum state as a real one and replacing it in situ would not be simple to achieve.
  2. Such new understanding can take unexpected forms. For example, recent work at the frontier of physics and computer science suggests that P!=NP can be taken as a new physical law. This law states that there exist problems whose solution can be verified in polynomial time but not found in polynomial time. In all known models of computation (including quantum computation and relativistic computation), no counterexample is known. By analogy, the nonexistence of perpetual motion led to the First and Second Laws of Thermodynamics in the 19th century. Much of what happens in the physical world can be formulated as problem solving (e.g., see D'Arcy Thompson's and Mandelbrot's work for many examples) where this law (or perhaps a more general version) applies. This would put an upper limit on how creative nature (e.g., evolution or human thinking) can be.
  3. When the hot-air balloon was invented in 1782 by the Montgolfier brothers, optimistic scientists quickly predicted that journeys to the moon were imminent. Apparently they did not realize that space is a vacuum and that balloons are supported by an atmosphere. Moon journeys did in fact take place, but two centuries later and through an enormous concerted effort.
  4. Let us make a first step to understand what an infinity barrier means. Consider a system with just two levels of abstraction, such as (chemistry, physics) or (biology, chemistry). The higher level is built using primitives from the lower level. The lower level says almost nothing about the higher level. To be precise, the computational expressiveness of the lower level is an upper bound to the computational expressiveness of the higher level. Beyond that, it is not possible to deduce what the higher level will do if you understand just the lower level. The higher level's functionality depends on historical accidents.
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